Superconformal partial waves have been so far computed in a number of examples, for various spacetime dimensions and types of correlators. There are several techniques of deriving them, which include making an ansatz as a sum of bosonic blocks and fixing coefficients using Ward identities [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, directly evaluating shadow integrals [10]} and solving the appropriate Casimir differential equations [11]}, [12]}, [13]}, [14]}, [15]}. What is common to these works is that they either focus on correlators of short operators so that the blocks have only one component, or otherwise restrict to the bottom component of blocks (by setting all Grassmann variables to zero). The bottom component takes the form of a finite sum of scalar bosonic blocks. It is desirable to extend the analysis and derive all components of superconformal blocks (termed long blocks) because they lead to a larger set of crossing equations for the same OPE data. First steps in this direction have been performed in [16]}, [17]}, [18]} where certain long blocks in 1-dimensional problems have been derived. As far as we know, the only computation of long blocks that is not ultimately reducible to one dimension was done in [19]}. It is expected that long blocks in general should be expressible as finite sums of spinning bosonic blocks.There is another, very general but less explicit, approach to superconformal partial waves proposed in [20]}.
